Algebra
Function Tables – Organising Input-Output Pairs
A function table lists several input-output pairs from a function machine side by side, usually as a column of x-values (inputs) and a column of y-values (outputs). Organising the pairs this way makes it easy to spot the pattern – and for a linear relationship, that pattern is always the same fixed difference between consecutive y-values.
A function table is also a direct bridge to the gradient concept: since the rate of change is constant for a linear relationship, you can calculate the gradient straight from any two rows of the table, using exactly the same gradient formula you use for two plotted points.
Working with Function Tables
To complete a table, apply the rule to each new input. To find the gradient from a table, use the gradient formula on any two (x, y) rows.
y = 3(6) − 2 = 18 − 2 = 16.
Gradient = (16 − 7) ÷ (5 − 2) = 9 ÷ 3 = 3.
Real-Life Application
- Price lists: a table showing cost for different quantities is a function table.
- Conversion charts: temperature or currency conversion charts are function tables.
- Timetables: a table of distance travelled at fixed time intervals is a function table.
Key Takeaways
- A function table lists input-output pairs generated by a rule.
- New table entries can be found by applying the rule to a new input.
- The gradient of a linear relationship can be calculated directly from any two table rows.